D O C . 1 G R A V I T A T I O N A L W A V E S 9 1. “On Gravitational Waves” [Einstein 1918a] Submitted 31 January 1918 Published 21 February 1918 In: Königlich Preußische Akademie der Wissenschaften (Berlin). Sitzungsberichte (1918): 154–167. The important question of how gravitational fields propagate was treated by me in an academy paper one and a half years ago.1 However, I have to return to the sub- ject matter since my former presentation is not sufficiently transparent and, further- more, is marred by a regrettable error in calculation. As before, I limit myself to the case where the space-time continuum that is un- der consideration deviates only very little from a “Galilean” one. In order to be able to write for all indices , (1) we select, as is customary in the special theory of relativity, the time variable as purely imaginary, i.e., we put , where denotes the “light time.” In (1) or depending upon or , respectively. The are small quantities compared to 1, and rep- resent the deviation of the continuum from one that is free of fields; under Lorentz transformations, they form a tensor of rank two. 1 These Sitzungsber. (1916), pp. 688 ff. [p. 154] [1] [2] [3] gμν –δμν γμν + = x4 it = t δμν 1 = δμν 0 = μ v = μ v ≠ γμν